(Please Help) The vertex of a parabola is (−2,8) and its y-intercept is (0,4). The parabola is the boundary of a quadratic inequality. The boundary is drawn with a solid line, and the exterior of the parabola is shaded.


What is the inequality represented?

(i got it graphed like what i have already but I don't know if its right even thought i gotten it)

\(~~~~~~ \stackrel{\textit{\Large Anna}}{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$100\\ r=rate\to 4.5\%\to \frac{4.5}{100}\dotfill &0.045\\ t=years\dotfill &3 \end{cases} \\\\\\ A=100[1+(0.045)(3)]\implies A=100(1.135)\implies A=113.5 \\\\[-0.35em] ~\dotfill\)

\(~~~~~~ \stackrel{\textit{\Large Matt}}{\textit{Simple Interest Earned Amount}} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$100\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &3 \end{cases} \\\\\\ A=100[1+(0.03)(3)]\implies A=100(1.09)\implies A=109 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Anna}{113.5} - \stackrel{Matt}{109}\implies 4.5\)

Thhe ratio of the planter's length to width is 4. Length : Width = 4 : 1

We are given that the ratio of the planter's width to height is 4. Mathematically, this can be expressed as:

w/h = 4

Substituting the expressions for w and h, we have:

(42 - 2x)/(18 - 2x) = 4

Let's solve the equation to find the exact value.

First, cross-multiply:

(42 - 2x) * 1 = (18 - 2x) * 4

42 - 2x = 72 - 8x

6x = 30

x = 5

Now we can substitute x = 5 into the expression (42 - 2x)/(18 - 2x):

(42 - 2(5))/(18 - 2(5)) = 32/8 = 4

Therefore, the ratio of the planter's length to width is 4. Length : Width = 4 : 1

Learn more about ratio on

https://brainly.com/question/12024093

#SPJ4

Each kennel should have dimensions of 35 feet by 45 feet to maximize the total enclosed area if no fencing is needed along the side of the building.

By considering the total area enclosed by all four kennels. Since they are identical, we can just focus on one kennel and multiply by four. Let the length of the kennel "L" and the width "W". We know that the perimeter of the kennel is 2L + 2W = 210 feet. We also know that we don't need any fencing along the side of the building, so one side of the kennel will be the building itself, which has length 120 feet. Therefore, we can write: 2L + W = 210 - 120 = 90

Solving for one variable in terms of the other, we get: L = 45 - 0.5W Now we want to maximize the area enclosed by the kennel. The area of a rectangle is simply length times width, so the area enclosed by one kennel is: A = LW = (45 - 0.5W)W = 45W -\(0.5W^2\)  

To find the maximum area, we can take the derivative of this expression with respect to W and set it equal to zero: dA/dW = 45 - W = 0 Solving for W, we get W = 45. Plugging this back into our equation for L, we get L = 35. Therefore, each kennel should have dimensions of 35 feet by 45 feet to maximize the total enclosed area.

To verify that this gives the maximum area, we can substitute these values into our expression for the area and simplify: A = LW = 35 * 45 = 1575 square feet per kennel. Total area = 4 * 1575 = 6300 square feet.

Learn more about kennel here:

https://brainly.com/question/28757976

#SPJ4

Answer: 12 and sqaure root of 194

Step-by-step explanation:

solution 1: 12 because if 13 is the missing side length of the hypotenuse then you would do 5^2 - 13^2 which is 169-25 = 144. the square root of 144 is 12

solution 2: the other solution is trying to get the hypotenuse. you would do 5^2 + 13^2 which is 25 + 169.. therefore the sum is 194. the answer would be the square root of 194

Answer:

Step-by-step explanation:

56.1,12.1,23.6

Answer: I mean- can you found it out yourself by studying. There's your answer.

Step-by-step explanation:

just study not cheat.

Answer: angle 5 =  55 degrees, angle 6 = 125 degrees, angle 7 = 55 degrees, angle 8 = 125 degrees

Answer:

C

Step-by-step explanation:

In order to find the slope, you can use rise over run.

(y₂ - y₁) over (x₂ - x₁)

You can use the points (1, 1) and (2, -1). y₂ can be -1 and y₁ can be 1, but you could do either as long as you make x₁ and x₂ from the corresponding points (so y₁ and x₁ are one coordinate pair and y₂ and x₂ are the other). This way, you get -2 as your slope. Then, the table shows that y = 3 when x is 0, so that's your y-intercept, which is how you get +3. Hope this helps!

y = -2x + 3 will be the equation represents the data in the table shown.

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. Sometimes, the aforementioned is referred to as a "linear equation of two variables," with y and x serving as the variables.

Given, A data Set of the value of x and y that represents a linear equation.

From the slope intercept form of a linear equation,

y = mx + b,

where m is the slope

b is the y-intercept

y- intercept is point in line where the value of x will be 0.

From our data set,

y - intercept = b = 3 (since, at x = 0, y is 3)

And Slope, (m) = (y₂ - y₁)/(x₂ - x₁)

in our case,

m = (1-3)/(1-0)(from first two values of data set)

m = -2

Thus,

Equation of line:

y = -2x + 3

Therefore, The equation of line for the given data set will be y = -2x + 3.

Learn more about Linear equation here:

https://brainly.com/question/11897796

#SPJ2

The two studies indicate that 150 minutes of intense exercise per week is effective in reducing mortality risks.

Study 1 was carried out by the National Cancer Institute and Harvard University, and they collected information about the exercise habits of around 661,000 middle-aged adults from six large ongoing health surveys. They then divided the data into various segments based on the weekly exercise time as a parameter.

The group with no exercise had the highest risk of premature death. Minimal exercise that is less than the recommended levels could still reduce the risk of premature death by 20%.

The group that followed the standard exercise guidelines of 150 min/week of moderate exercise had a 31% lower probability of premature death. Individuals who exercised three times the recommended levels had the best benefits, with a 39% reduction in the risk of premature death.

However, increasing the exercise time did not have a significant effect on mortality risk rates. Study 2 was conducted by James Cook University in Cairns. They collected health survey data for over 200,000 Australian adults, which was then analyzed with corresponding death statistics. Their analysis was more detailed than the first study since they divided the data according to exercise stress levels ranging from normal to strenuous.

The results were similar to the first study, but there were some additional findings. The study showed that adhering to the general recommended exercise guidelines substantially decreased the risk of premature death, even with moderate exercise like walking. Intense exercise had little to no effect on mortality rates.

However, those who spent up to 30 percent of their weekly exercise time in vigorous activities were 9 percent less likely to die prematurely. With more than 30% of their time dedicated to strenuous activities, people gained an extra 13% reduction in early mortality, compared with people who stuck to moderate exercise levels. Very high levels of intense exercise did not improve mortality risk rates significantly.

In conclusion, the two studies indicate that 150 minutes of intense exercise per week is effective in reducing mortality risks.

learn more about mortality risks here:

https://brainly.com/question/4689314

#SPJ11

Answer:

Parallelogram

Step-by-step explanation:

a quadrilateral (4 sides figure) whose opposite sides are parallel.  The opposite sides have the same length and opposite angles are equal.

Helping in the name of Jesus.

a) The perimeter of the cross is: P = 4a = 4(c - b) = 4c - 4b

b) The area of the cross is:\(A= 2cb - 2b^2 \ cm^2\)

c) b in terms of A and C is: \(b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}\)

What is area and perimeter?

The perimeter of a shape is the distance around its outside. The space inside a shape is measured by area.

a) The perimeter, P, of the cross is equal to the sum of the lengths of its four arms.

The length of one arm of the cross can be found by subtracting the length of one rectangle from the length of the other rectangle. Since each rectangle has dimensions c cm × b cm, the length of one arm is:

a = c - b

Therefore, the perimeter of the cross is:

P = 4a = 4(c - b) = 4c - 4b

b) The area, A, of the cross is equal to the area of the two rectangles minus the area of the four triangles formed by the arms of the cross.

The area of each rectangle is:

\(Area_{rect} = c * b\)

The area of each triangle is:

\(Area_{tri} = (a * b) / 2 \\\\= \frac{[(c - b) * b]}{2} \\\\= \frac{ (c * b - b^{2} )}{2}\)

Since there are four triangles, the total area of the triangles is:

\(4A_{tri} = 2cb - 2b^2\ cm^2\)

Therefore, the area of the cross is:

\(A = 2A_{rect} - 4A_{rect} \\\\ = 2cb - 2b^2\)

c) c) To find b in terms of A and C, we can use the formula for the area of the cross that we found in part b:

\(A = 2cb - 2b^2\)

We can rearrange this equation to put it in the form of a quadratic equation:

\(2b^2 - 2cb + A = 0\)

This is a quadratic equation in standard form, with a = 2, b = -2c, and c = A. We can use the quadratic formula to solve for b:

b = (-b ± sqrt(b^2 - 4ac)) / 2a

b = (2c ± sqrt((2c)^2 - 4(2)(A))) / (2 × 2)

\(b=\frac{-b ± \sqrt{(b^2 - 4ac)} }{2a} \\\\b= \frac{2c ± \sqrt{(2c^2 - 4(2)c)}}{4} \\\\b= \frac{2c ± \sqrt{(4c^2 - 16A)}}{4} \\\\b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}\)

Therefore, b in terms of A and C is: \(b= \frac{c ± \sqrt{(c^2 - 4A)}}{2}\)

To know more about area and perimeter visit,

https://brainly.com/question/29146069

#SPJ1

Answer:

24 yards of chain were sold

Step-by-step explanation:

1 ft = 1/3 yd

72 * 1/3 = 24

The solution to x² - 9x < -18 is x < -6 or x > 3 (Option A).

To solve the inequality x² - 9x < -18, we need to find the values of x that satisfy the given inequality.

1: Move all terms to one side of the inequality:

x² - 9x + 18 < 0

2: Factor the quadratic equation:

(x - 6)(x - 3) < 0

3: Determine the sign of the expression for different intervals:

Interval 1: x < 3

For x < 3, both factors (x - 6) and (x - 3) are negative. A negative multiplied by a negative gives a positive, so the expression is positive in this interval.

Interval 2: 3 < x < 6

For 3 < x < 6, the factor (x - 6) becomes negative, while the factor (x - 3) remains positive. A negative multiplied by a positive gives a negative, so the expression is negative in this interval.

Interval 3: x > 6

For x > 6, both factors (x - 6) and (x - 3) are positive. A positive multiplied by a positive gives a positive, so the expression is positive in this interval.

4: Determine the solution:

The expression is negative only in the interval 3 < x < 6. Therefore, the solution to x² - 9x < -18 is x < -6 or x > 3, which corresponds to option A.

For more such questions on solution, click on:

https://brainly.com/question/24644930

#SPJ8

Answer:

60 degrees counterclockwise

Step-by-step explanation:

One circle is 360 degrees.

If the circle is split into 6 pieces, (360/6 = 60), then each piece is 60 degrees, like in the example.

Answer:

60 degrees counterclockwise

Step-by-step explanation:

The probability that x is less than 5 = 0.45

Discrete probability distribution:

It is a type of probability distribution that displays all the possible values of a discrete random variable accompanying the affiliated probabilities. We can also say that a discrete probability distribution provides the chance of occurrence of every possible value of a discrete random variable.

Discrete probability distribution:

x          = -10      0       10        20

P(X=x) = 0.35  0.10   0.15     0.40

The probability that x is less than 5:

P(X<5) = 1 - P (X = 10) - P(X= 20)

1 - 0.15 - 0.40 = 0.45

The probability that x is less than 5 is = 0.45

Learn more about probability from:

https://brainly.com/question/23017717

#SPJ4

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

A. Understand

The question is asking how much money is saved.

Given :

B. Plan

that is :

C. Solve

Hence, savings = Php 3544.55

To test the claim Hₐ: μ = 55.6 at a significance level of α = 0.05, using a sample of size n = 24 with a sample mean x = 65.8 and a sample standard deviation s = 17.9, the p-value for this sample is approximately 0.0066, accurate to four decimal places.

The p-value is a measure of the evidence against the null hypothesis (H₀) based on the observed data. It represents the probability of obtaining a sample mean as extreme as, or more extreme than, the observed mean, assuming the null hypothesis is true.

In this case, we want to determine the p-value for the sample mean of 65.8, given the null hypothesis μ = 55.6 and the sample standard deviation s = 17.9.

To calculate the p-value, we can use the t-distribution since the population standard deviation is unknown. We calculate the test statistic (t-value) using the formula:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

t = (65.8 - 55.6) / (17.9 / sqrt(24))

t ≈ 1.8016

Next, we find the p-value associated with this t-value using a t-distribution table or statistical software. The p-value is the probability of observing a t-value as extreme as 1.8016 or more extreme, in either tail of the distribution.

For a two-tailed test, the p-value is approximately 0.0066.Therefore, the p-value for this sample is approximately 0.0066, indicating strong evidence against the null hypothesis.

Learn more about mean here:

https://brainly.com/question/31098693

#SPJ11  

The odd function drawn in this problem is given as follows:

f(x) = x³.

The line of symmetry is given as follows:

x = 0.

More can be learned about odd functions at https://brainly.com/question/2284364

#SPJ1

The probability that a student scored is 0.8.

To find the probability that a student scored less than 600 or took less than 4 years of math.

We need to add the probabilities of each of these events occurring separately, and then subtract the probability of both events occurring together.

Let P(L) be the probability that a student scored less than 600 and P(M) be the probability that a student took less than 4 years of math.

We are not given the joint probability of both events, so we need to calculate it using the formula:

P(L and M) = P(L) + P(M) - P(L or M)

where P(L or M) is the probability that a student scored less than 600 or took less than 4 years of math.

Assuming that the events of scoring less than 600 and taking less than 4 years of math are independent, we can calculate their probabilities separately:

P(L) = 0.35 (given)

P(M) = 0.25 (given)

To calculate P(L or M), we add the probability of scoring less than 600 to the probability of taking less than 4 years of math, and then subtract the probability of both events occurring together:

P(L or M) = P(L) + P(M) - P(L and M)

We don't have the value of P(L and M), so we cannot directly calculate P(L or M). However, we know that the sum of probabilities of all possible events is equal to 1.

Therefore, we can use the formula:

P(not L and not M) = 1 - P(L or M)

where P(not L and not M) is the probability that a student scored 600 or more and took 4 or more years of math.

Since we know that the events of not scoring less than 600 and taking 4 or more years of math are complementary to scoring less than 600 or taking less than 4 years of math.

We can use the complement rule to calculate P(not L and not M):

P(not L and not M) = 1 - P(L or M)

= 1 - (P(L) + P(M) - P(L and M))

= 1 - (0.35 + 0.25 - P(L and M))

= 0.4 - P(L and M)

Now we need to find P(L and M) to calculate P(not L and not M). We are not given this probability directly, so we cannot use the product rule.

However, we know that the number of students who scored less than 600 and took less than 4 years of math is 80, and the total number of students is 400. Therefore, we can use the formula:

P(L and M) = number of students who scored less than 600 and took less than 4 years of math / total number of students

= 80 / 400

= 0.2

Substituting this value in the formula for P(not L and not M), we get:

P(not L and not M) = 0.4 - P(L and M)

= 0.4 - 0.2

= 0.2

Therefore, the probability that a student scored less than 600 or took less than 4 years of math is:

P(L or M) = 1 - P(not L and not M)

= 1 - 0.2

= 0.8

So the probability that a student scored less than 600 or took less than 4 years of math is 0.8.

Learn more about probability

brainly.com/question/29381779

#SPJ11

Answer:

13 + 12√2

Step-by-step explanation:

Not sure if there's an easier way, but here's my method:

Draw the radius lines from the center of the circle to each vertex of the octagon.  This will divide the octagon into 8 isosceles triangles, 4 big and 4 small.

Draw the height of one of the big triangles.  Define the angle between the height and the radius as A.  Similarly, draw the height of one of the small triangles.  Define the angle between the height and the radius as B.

Using trig, we can say:

sin A = 1.5 / r

sin B = 1 / r

The vertex angle of the large isosceles triangle is 2A, and the vertex angle of the small isosceles triangle is 2B.  Therefore:

4(2A) + 4(2B) = 360

A + B = 45

If we substitute into the first trig equation:

sin(45 − B) = 1.5 / r

sin 45 cos B − cos 45 sin B = 1.5 / r

1/√2 cos B − 1/√2 (1/r) = 1.5 / r

cos B − 1/r = 1.5√2 / r

cos B = (1 + 1.5√2) / r

If we substitute into the second trig equation:

sin(45 − A) = 1 / r

sin 45 cos A − cos 45 sin A = 1 / r

1/√2 cos A − 1/√2 (1.5/r) = 1 / r

cos A − 1.5/r = √2 / r

cos A = (1.5 + √2) / r

Using SAS area of a triangle, the area of the large triangle is:

Area = ½ r² sin(2A)

Area = ½ r² (2 sin A cos A)

Area = r² sin A cos A

Area = (r sin A) (r cos A)

Area = (1.5) (1.5 + √2)

Area = 2.25 + 1.5√2

Similarly, the area of a small triangle is:

Area = ½ r² sin(2B)

Area = ½ r² (2 sin B cos B)

Area = r² sin B cos B

Area = (r sin B) (r cos B)

Area = (1) (1 + 1.5√2)

Area = 1 + 1.5√2

So the total area is:

Area = 4(2.25 + 1.5√2) + 4(1 + 1.5√2)

Area = 9 + 6√2 + 4 + 6√2

Area = 13 + 12√2

The coordinates of point D 0.25 x-axis for the points A(2, 6), B(0, 0), C(-5, 8), and D(-2, 10) are (-2, -2.5) when point D is reflected across the x-axis. This is obtained by negating the y-coordinate of point D and keeping the x-coordinate the same.

To find the coordinates of point D 0.25 x-axis, we need to reflect point D across the x-axis. This will result in the y-coordinate of point D being negated while the x-coordinate remains the same.

The coordinates of point D are (-2, 10), so when we reflect it across the x-axis, we get the new coordinates:

D 0.25 x-axis = (-2, -10/4) = (-2, -2.5)

Therefore, the coordinates of point D0.25∘rx-axis for the given points A, B, C, and D are (-2, -2.5).

Learn more about graphs here: brainly.com/question/17267403

#SPJ4

Answer:

288 cm^3

Step-by-step explanation:

The value of k that makes the function continuous is k = 5 = 1.

To find the value of k that makes the function continuous, let's consider a function defined by different pieces:

\(\[ f(x) = \begin{cases} x^2 + 1 & \text{if } x < 2 \\ k & \text{if } x = 2 \\ 2x - 3 & \text{if } x > 2 \\ \end{cases}\]\)

For the function to be continuous at x = 2, we need the following conditions to be satisfied:

1. The limit of f(x) as x approaches 2 from the left (x < 2) should be equal to the value of f(x) at x = 2.

2. The limit of f(x) as x approaches 2 from the right (x > 2) should be equal to the value of f(x) at x = 2.

Let's evaluate these limits:

\(\[\lim_{{x \to 2^-}} (x^2 + 1) = 2^2 + 1 = 5\]\\$\[\lim_{{x \to 2^+}} (2x - 3) = 2(2) - 3 = 1\]\)

To ensure continuity, these limits must be equal to the value of f(x) at x = 2, which is k. Therefore, we have k = 5 = 1.

Hence, the value of k that makes the function continuous is k = 5 = 1.

Complete Question - Find the value of k that makes the function continuous by considering a function defined by different pieces.

To know more about continuous functions, refer here:

https://brainly.com/question/30464564#

#SPJ11

Answer:

X+3y-15=0

Step-by-step explanation:

not really sure (pls don't come at me if wrong)

Answer:

Domain: (-3, 1]

Range: [-4, 0)

Step-by-step explanation:

Domain is all the x-values that can be plugged into the graph.

Range is all y-values that are outputted from inputting x.

We can see that our x-values span from -3 to 1. Since -3 is open dot, it is not included. Brackets signify inclusion.

(-3, 1]

We can see that our y-values span from -4 to 0. Since when x = -3 is open dot, the output y = 0 is also not included.

[-4, 0)

Deep foundations are recommended for larger or hillside developments , or those on poor soil .

Foundation Systems in Building

There are two classifications of foundations in building shallow foundations and deep foundations . These categories refer to the depth of soil in which the foundation is formed .

Shallow Foundations : Shallow foundations are usually located less than six feet below the lowest finished floor of a structure.

Deep Foundations : Deep foundations are structural elements that are used to transfer loads from weak and compressible soils to a stronger layer, usually located at a significant depth below the ground.

Recommendation

A shallow foundation can be constructed in as little as a one-foot depth , whereas a deep foundation is formed at a depth of 10 - 300 feet . Deep foundations are recommended for larger or hillside developments , or those on poor soil .

To learn more on foundations follow link :

https://brainly.com/question/28723911

#SPJ4

Answer:

Step-by-step explanation: A shallow foundation distributes loads from the building into the upper layers of the ground.

Shallow foundations perform very well on sites with strong soils, sufficiently thick natural gravel rafts overlying weaker soils or where robust, engineered ground improvement is carried out.

Deep foundations can provide a good foundation for houses on sites with poor soil conditions near the surface,

The given statement is False. A test statistic based on point estimation is not used to construct the decision rule which defines the rejection region.

In hypothesis testing, a test statistic is calculated using sample data and a specific hypothesis to assess the strength of evidence against the null hypothesis. The decision rule, which determines whether to reject or fail to reject the null hypothesis, is based on the test statistic's distribution under the null hypothesis, rather than the point estimate itself.

The construction of the decision rule involves selecting a significance level (alpha), which represents the probability of rejecting the null hypothesis when it is actually true. The rejection region is determined based on the chosen significance level and the distribution of the test statistic. If the calculated test statistic falls within the rejection region, the null hypothesis is rejected; otherwise, it is not rejected.

Point estimation, on the other hand, is used to estimate an unknown parameter of interest, such as the population mean or proportion, based on sample data. It involves calculating a single value (point estimate) that represents the best guess for the parameter value. The point estimate is not directly involved in constructing the decision rule or defining the rejection region in hypothesis testing.

Learn more about test statistic here:

https://brainly.com/question/31746962

#SPJ11

False. A test statistic based on point estimation is not used to construct the decision rule that defines the rejection region.

The process of hypothesis testing involves constructing a decision rule to determine whether to accept or reject a null hypothesis based on sample data. The decision rule is typically defined using a critical region or rejection region, which is a range of values for the test statistic.

Point estimation, on the other hand, is a method used to estimate an unknown population parameter based on sample data. It involves calculating a single value (point estimate) that serves as an estimate of the population parameter.

While point estimation and hypothesis testing are both important concepts in statistics, they serve different purposes. Point estimation is used to estimate population parameters, whereas hypothesis testing involves making decisions based on sample data.

The decision rule for hypothesis testing is typically constructed based on the significance level (alpha) and the distribution of the test statistic, such as the t-distribution or the standard normal distribution. The test statistic is calculated using sample data and compared to critical values or calculated p-values to determine whether to reject the null hypothesis.

Therefore, the statement that a test statistic based on point estimation is used to construct the decision rule defining the rejection region is false.

Learn more about  statistic here:

https://brainly.com/question/32201536

#SPJ11

Answer:

the other two factors, (2x+1)(3x+1)

Step-by-step explanation:

(a + 1)x³ + (2 – 3a)x² – (3a – 1)x + 2a – 13 = 0   ...(1)

x-3 = 0     x = 3  

(a + 1)*3³ + (2 – 3a)*3² – (3a – 1)*3 + 2a – 13 = 0

-7a + 35 = 0

a = 5   .. substitute to (1)

6x³ -13x² – 14x -3 = 0

(x-3)(6x²+px+1) = 0 ..... 1*x * 6x² = 6x³,    -3 * 1 = -3

6x³ +(p-18)x² +(1-3p)x -3 = 0

p-18 = -13

p = 5

6x²+5x+1 = (2x+1)(3x+1)